%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO502+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:01 AM UTC 2026
% Result : Theorem 0.14s 5.79s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 128 ( 57 ~; 53 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-7 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 67 ( 4 sgn 28 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz7_22b,axiom,
! [Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2] :
( s_t(Xm1,Xc,Xm2)
| ~ s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) ),
file('theBenchmark.p',aSatz7_22b) ).
fof(d_Defn7_23,axiom,
! [Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2] :
( ( s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)
| ~ s_m(Xa2,Xm2,Xb2)
| ~ s_m(Xa1,Xm1,Xb1)
| ~ s_e(Xc,Xa2,Xc,Xb2)
| ~ s_e(Xc,Xa1,Xc,Xb1)
| ~ s_t(Xb1,Xc,Xb2)
| ~ s_t(Xa1,Xc,Xa2) )
& ( s_m(Xa2,Xm2,Xb2)
| ~ s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) )
& ( s_m(Xa1,Xm1,Xb1)
| ~ s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) )
& ( s_e(Xc,Xa2,Xc,Xb2)
| ~ s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) )
& ( s_e(Xc,Xa1,Xc,Xb1)
| ~ s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) )
& ( s_t(Xb1,Xc,Xb2)
| ~ s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) )
& ( s_t(Xa1,Xc,Xa2)
| ~ s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) ) ),
file('theBenchmark.p',d_Defn7_23) ).
fof(aSatz7_22,conjecture,
! [Xa1,Xc,Xa2,Xb1,Xb2,Xm1,Xm2] :
( s_t(Xm1,Xc,Xm2)
| ~ s_m(Xa2,Xm2,Xb2)
| ~ s_m(Xa1,Xm1,Xb1)
| ~ s_e(Xc,Xa2,Xc,Xb2)
| ~ s_e(Xc,Xa1,Xc,Xb1)
| ~ s_t(Xb1,Xc,Xb2)
| ~ s_t(Xa1,Xc,Xa2) ),
file('theBenchmark.p',aSatz7_22) ).
fof(aSatz7_22_neg,negated_conjecture,
~ ! [Xa1,Xc,Xa2,Xb1,Xb2,Xm1,Xm2] :
( s_t(Xm1,Xc,Xm2)
| ~ s_m(Xa2,Xm2,Xb2)
| ~ s_m(Xa1,Xm1,Xb1)
| ~ s_e(Xc,Xa2,Xc,Xb2)
| ~ s_e(Xc,Xa1,Xc,Xb1)
| ~ s_t(Xb1,Xc,Xb2)
| ~ s_t(Xa1,Xc,Xa2) ),
inference(assume_negation,[status(cth)],[aSatz7_22]) ).
cnf(c_142,plain,
( s_kf(A,F,D,B,E,V6,C)
| ~ s_m(C,V6,E)
| ~ s_m(A,F,D)
| ~ s_e(B,C,B,E)
| ~ s_e(B,A,B,D)
| ~ s_t(D,B,E)
| ~ s_t(A,B,C) ),
inference(clausify,[status(thm)],[d_Defn7_23]) ).
cnf(c_149,plain,
( s_t(B,D,F)
| ~ s_kf(A,B,C,D,E,F,V6) ),
inference(clausify,[status(thm)],[aSatz7_22b]) ).
fof(nnf_123,plain,
? [Xa1,Xc,Xa2,Xb1,Xb2,Xm1,Xm2] :
( ~ s_t(Xm1,Xc,Xm2)
& s_m(Xa2,Xm2,Xb2)
& s_m(Xa1,Xm1,Xb1)
& s_e(Xc,Xa2,Xc,Xb2)
& s_e(Xc,Xa1,Xc,Xb1)
& s_t(Xb1,Xc,Xb2)
& s_t(Xa1,Xc,Xa2) ),
inference(fof_nnf,[status(thm)],[aSatz7_22_neg]) ).
fof(sk_aSatz7_22_neg,plain,
( ~ s_t(sK5,sK1,sK6)
& s_m(sK2,sK6,sK4)
& s_m(sK0,sK5,sK3)
& s_e(sK1,sK2,sK1,sK4)
& s_e(sK1,sK0,sK1,sK3)
& s_t(sK3,sK1,sK4)
& s_t(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(Xa1,sK0),skolemize(Xc,sK1),skolemize(Xa2,sK2),skolemize(Xb1,sK3),skolemize(Xb2,sK4),skolemize(Xm1,sK5),skolemize(Xm2,sK6)],[nnf_123]) ).
cnf(c_317,negated_conjecture,
s_t(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_aSatz7_22_neg]) ).
cnf(c_318,negated_conjecture,
s_t(sK3,sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_aSatz7_22_neg]) ).
cnf(c_319,negated_conjecture,
s_e(sK1,sK0,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_aSatz7_22_neg]) ).
cnf(c_320,negated_conjecture,
s_e(sK1,sK2,sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_aSatz7_22_neg]) ).
cnf(c_321,negated_conjecture,
s_m(sK0,sK5,sK3),
inference(split_conjunct,[status(thm)],[sk_aSatz7_22_neg]) ).
cnf(c_322,negated_conjecture,
s_m(sK2,sK6,sK4),
inference(split_conjunct,[status(thm)],[sk_aSatz7_22_neg]) ).
cnf(c_323,negated_conjecture,
~ s_t(sK5,sK1,sK6),
inference(split_conjunct,[status(thm)],[sk_aSatz7_22_neg]) ).
cnf(c_325,plain,
( s_t(F,B,V6)
| ~ s_m(C,V6,E)
| ~ s_m(A,F,D)
| ~ s_e(B,C,B,E)
| ~ s_e(B,A,B,D)
| ~ s_t(D,B,E)
| ~ s_t(A,B,C) ),
inference(resolve,[status(thm)],[c_142,c_149]) ).
cnf(c_1402,negated_conjecture,
( s_t(C,sK1,D)
| ~ s_m(sK2,D,B)
| ~ s_m(sK0,C,A)
| ~ s_e(sK1,sK2,sK1,B)
| ~ s_e(sK1,sK0,sK1,A)
| ~ s_t(A,sK1,B) ),
inference(resolve,[status(thm)],[c_325,c_317]) ).
cnf(c_1403,negated_conjecture,
( s_t(A,sK1,B)
| ~ s_m(sK2,B,sK4)
| ~ s_m(sK0,A,sK3)
| ~ s_e(sK1,sK2,sK1,sK4)
| ~ s_e(sK1,sK0,sK1,sK3) ),
inference(resolve,[status(thm)],[c_1402,c_318]) ).
cnf(c_1404,negated_conjecture,
( s_t(A,sK1,B)
| ~ s_m(sK2,B,sK4)
| ~ s_m(sK0,A,sK3)
| ~ s_e(sK1,sK2,sK1,sK4) ),
inference(resolve,[status(thm)],[c_1403,c_319]) ).
cnf(c_1405,negated_conjecture,
( s_t(A,sK1,B)
| ~ s_m(sK2,B,sK4)
| ~ s_m(sK0,A,sK3) ),
inference(resolve,[status(thm)],[c_1404,c_320]) ).
cnf(c_1406,negated_conjecture,
( s_t(sK5,sK1,A)
| ~ s_m(sK2,A,sK4) ),
inference(resolve,[status(thm)],[c_1405,c_321]) ).
cnf(c_1407,negated_conjecture,
s_t(sK5,sK1,sK6),
inference(resolve,[status(thm)],[c_1406,c_322]) ).
cnf(c_1401,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_323,c_1407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO502+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 13:36:48 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 3030117 was started by sandbox2 on n006,
% 0.09/5.38 % Fri Sep 25 13:36:48 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.41
% 0.14/5.41 % From the command line: assign(max_seconds, 300).
% 0.14/5.79
% 0.14/5.79 % SZS status Theorem for theBenchmark
% 0.14/5.79
% 0.14/5.79 % Proof 1 at 0.26 (+ 0.11) seconds.
% 0.14/5.79 % Length of proof is 14.
% 0.14/5.79 % Level of proof is 3.
% 0.14/5.79 % Maximum clause weight is 35.000.
% 0.14/5.79 % Given clauses 150.
% 0.14/5.79
% 0.14/5.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------